Numbers- Introduction to Multiplication and Division
Topic: Multiplication and Division What is multiplication? Multiplication is taking one number and then adding it together a specified number of times.
Lets look at a example: 3 multiplied by 5 = 3+3+3+3+3 or
5 multiplied by 4 = 5 + 5 + 5 + 5 = 20
We took the number 3 and added it together 5 times. This is why multiplication is sometimes called "times". For example we sometimes says "times table" instead of "Multiplication table".
Multiplication is usually represented by the symbol "x" but can also be represented by the symbol "*"
Here are examples below on how to use the symbols
-
5 x 4 -
5 * 4 -
5 times 4
Important terms to be aware of when using multiplication Factors and Products
Factors are the numbers that you are multiplying together while Products are the answers.
(factor) x (factor) = product Example: 2(factor) × 5 (factor)= 10(product)
There are special rules to remember when multiplying using zeros (0) and ones (1).
When multiplying by 0, the answer is always 0.
Examples:
-
12 x 0 = 0 -
7676 x 0 = 0 -
15 × 0 = 0
When multiplying by 1, the answer is always the same as the number multiplied by 1.
Examples:
-
1 x 60 = 60 -
1 x 1 = 1 -
1 x 0 = 0 -
12 × 1 = 12
An important rule to remember with multiplication is that the order you multiply numbers is not important. The order in which you multiply them does not matter the answer will be the same.
Examples:
1. 3 x 2 = 2 + 2 + 2 = 6 2. 2 x 3 = 3 + 3 = 6 1. 6 x 1 = 1 + 1 + 1 + 1 + 1 + 1 = 6 2. 1 x 6 = 6 = 6 What is division?
Division is breaking a number up into an equal number of parts.
Example:
20 divided by 4 = ?
If you take 20 things and put them into four equal sized groups, there will be 5 things in each group. The answer is 5.
20 divided by 4 = 5.
The mainly used division symbol is "÷" but other another commonly used symbol is the backslash "/". It can also be written in fraction form with one number above the other.
Example signs for "a divided by b":
a ÷ b
a/b
a b
When dividing some important words to be aware of are dividend, the divisor and quotient. 1. Dividend - The dividend is the number you are dividing up 2. Divisor - The divisor is the number you are dividing by 3. Quotient - The quotient is the answer Dividend ÷ Divisor = Quotient Example:
In the problem 10 ÷ 2 = 5
Dividend = 10
Divisor = 2
Quotient = 5
Important Notes to remember
1. Dividing by 1 When dividing something by 1, the answer is the original number. In other words, if the divisor is 1 then the quotient equals the dividend.
Examples:
8 ÷ 1 = 8
78.2 ÷ 1 = 78.2
2. Dividing by 0 You cannot divide a number by 0. The answer to this question is undefined. If you should try to divide using zero (0) on a calculator an error message would pop up.
3) Dividend equals Divisor If the dividend and the divisor are the same number (and not 0), then the answer is always 1.
Examples:
16 ÷ 16 = 1
20.5 ÷ 20.5 = 1
When the answer to a division problem is not a whole number, the "leftovers" are called the remainder.
For example, if you were to try and divide 20 by 3 you would discover that 3 does not divide evenly into 20. The closest numbers to 20 that 3 can divide into are 18 and 21. You pick the closest number that 3 divides into that is smaller than 20. That is 18.
18 divided by 3 = 6, but there are still some leftovers. 20 -18 = 2. There are 2 remaining.
We write the remainder after an "r" in the answer.
20 ÷ 3 = 6 r 2
It must be quite clear by now that division is the opposite of multiplication.
Another way to think of division is as the opposite of multiplication. Let's look at the following example
20 ÷ 4 = 5
You can do the reverse, replacing the = with a x sign and the ÷ with an equal sign:
5 x 4 = 20
For a quick recap watch the video below